If you don't use TestFlight, each user's device will need to be explicitly added to your provisioning profiles -- before you build the app. Apple allows a max of 100 device UDID's of each type (iPhone, iPad, iPod) per year. You can deactivate a UDID, but it remains part of your 100 maximum for that type until your next Apple developer account anniversary.

Anyway, if you collect their UDID values and add to your provisioning profiles, then you can allow them to download and install over the air from their own device. The app has to be hosted on a HTTPS connection (starting with iOS 7 or so?) but dropbox qualifies. However, it can't be a link to the *.ipa itself. It has to be a link to a special *.plist file which among other things lists the *.ipa location.

The other potential methods are jail break the devices or Apple Enterprise License. But those are really for in-house use, not outside beta testers. It isn't a viable method for what you are asking. I'm mentioning it only because it is another way to install apps. In fact, nearly all of my own apps are installed that way for clients.